Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient

Luis Silvestre

doi:10.3934/dcds.2010.28.1069

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2010, Volume 28, Issue 3: 1069-1081. Doi: 10.3934/dcds.2010.28.1069

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Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient

Luis Silvestre^1,

1.
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637

Received: February 28, 2010

Revised: March 31, 2010

Published: August 2010

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Abstract

We prove that the solution to a parabolic integro-differential equation with a gradient dependence that satisfies a critical power growth becomes immediately Hölder continuous. We also obtain some results in the supercritical case.

Keywords:

parabolic equations integro-differential equations. Hölder regularity..

Mathematics Subject Classification: Primary: 35R09, 35B65.

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